The Wife's Lament has generated multiple interpretations. If only, as M-R claim, 'common sense' were a curb to these 'ingenious explanations'.
The most fundamental question criticism has asked is whether the speaker is a woman. The evidence is quite thin: three adjectival endings in the first two lines of the poem and the supposed 'differentness of language' (Belanoff, 1990) typical of women's songs. The identification of a female narrator has lead critics to read the poem in the context of continental Frauenleider (Malone 1962) and Latin erotic poetry circulating in Anglo-Saxon England (Davidson 1975). Alternatively, the identification of a male narrator allows the poem to be read alongside The Wanderer and The Seafarer as an expression of the speaker's sadness at the breaking of the comitatus-bond (Bambas 1963, Stevens 1968, Mandel 1987). Stevens may be right that 'there is not a single word in the entire poem which has purely feminine connotations'.
Other critics have directed their attentions to solving perceived 'difficulties' in the poem. Most of the speculation has proceeded from the striking and concrete description of the narrator's environment. Does eorðscræf mean grave and is the narrator therefore dead (Lench 1970, Tripp 1972, Johnson 1983)? Do the actreo and herh indicate that the wife is dwelling in a place holy to pagans (Doane 1966, Wentersdorf 1981). Wentersdorf's article is actually one of the more sensitive essays to have been written about the poem and makes it clear that eleventh-century Christians understood the significance of pre-Christian religious sites.
It is remarkable that a criticism so voluminous has covered so few bases. Little historical criticism has been attempted (though Schaefer 1986 is an exception), probably because bards seem more interesting than scribes. It's a severe handicap to historical criticism not to know when the supposed 'original' was written. What if the extant copy were the only copy that ever existed? For information only, since the metrical tests and grand narratives on which the dating and localisation is based are totally unconvincing, the poet was writing in the eighth century and was probably writing in Mercia, perhaps near the Welsh border.